library(rstan)
library(survival)
library(tidyverse)
library(tidybayes)
library(scales)
library(survminer)
Stan_exponential_survival_model <- "
data{
int <lower=1> N_uncensored;
int <lower=1> N_censored;
int <lower=0> numCovariates;
matrix[N_censored, numCovariates] X_censored;
matrix[N_uncensored, numCovariates] X_uncensored;
vector <lower=0>[N_censored] times_censored;
vector <lower=0>[N_uncensored] times_uncensored;
}
parameters{
vector[numCovariates] beta; //regression coefficients
real alpha; //intercept
}
model{
beta ~ normal(0,10); //prior on regression coefficients
alpha ~ normal(0,10); //prior on intercept
target += exponential_lpdf(times_uncensored | exp(alpha+X_uncensored * beta)); //log-likelihood part for uncensored times
target += exponential_lccdf(times_censored | exp(alpha+X_censored * beta)); //log-likelihood for censored times
}
generated quantities{
vector[N_uncensored] times_uncensored_sampled; //prediction of death
for(i in 1:N_uncensored) {
times_uncensored_sampled[i] = exponential_rng(exp(alpha+X_uncensored[i,]* beta));
}
}
"
# prepare the data
set.seed(42);
require (tidyverse);
data <- read_csv('../data/necessary_fields.csv')
Rows: 2066 Columns: 7
── Column specification ────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Delimiter: ","
chr (1): host_type
dbl (1): duration_months
lgl (5): major_releases, censored, high_rev_freq, multi_repo, high_author_count
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
N <- nrow (data);
data$major_releases <- car::recode(data$major_releases, "'TRUE' = 0; 'FALSE' = 1")
data$censored <- car::recode(data$censored, "'TRUE' = 0; 'FALSE' = 1")
X <- as.matrix(pull(data, major_releases));
is_censored <- pull(data, censored)== 0;
times <- pull(data, duration_months);
msk_censored <- is_censored == 1;
N_censored <- sum(msk_censored);
Stan_data <- list (N_uncensored = N - N_censored,
N_censored = N_censored,
numCovariates = ncol(X),
X_censored = as.matrix(X[msk_censored,]),
X_uncensored = as.matrix(X[!msk_censored ,]),
times_censored = times[msk_censored],
times_uncensored = times[!msk_censored])
# Fit Stan model
require(rstan)
exp_surv_model_fit <- suppressMessages(stan(model_code = Stan_exponential_survival_model, data = Stan_data))
sh: Data/bayesian: No such file or directory
sh: clang++ -mmacosx-version-min=10.13: command not found
Warning in system2(CXX, args = ARGS) : error in running command
Warning in file.remove(c(unprocessed, processed)) :
cannot remove file '/var/folders/q8/7tchbyvd1dj3hkgw5ffkk6ph0000gp/T//RtmpHtsCUK/file985c8a5369f.stan', reason 'No such file or directory'
SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 1).
Chain 1:
Chain 1: Gradient evaluation took 0.000286 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 2.86 seconds.
Chain 1: Adjust your expectations accordingly!
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SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 2).
Chain 2:
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SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 3).
Chain 3:
Chain 3: Gradient evaluation took 0.000184 seconds
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SAMPLING FOR MODEL 'bf5dbbde6a245330de71a285e3fe7c42' NOW (CHAIN 4).
Chain 4:
Chain 4: Gradient evaluation took 0.0002 seconds
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print(get_seed(exp_surv_model_fit))
[1] 1781592037
fit_summary <- summary(exp_surv_model_fit)
print(fit_summary$summary)
mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
beta[1] 1.068763 0.005816100 0.1444464 0.790465 0.9761651 1.067160 1.158581 1.373116 616.8074 1.0071725
alpha -5.773486 0.005579162 0.1389656 -6.062658 -5.8602008 -5.772233 -5.682895 -5.509260 620.4070 1.0076445
times_uncensored_sampled[1] 110.243140 1.736177866 110.5102633 3.004338 31.2820284 76.183068 154.169910 398.796930 4051.5089 1.0002822
times_uncensored_sampled[2] 108.947259 1.726552927 108.4249757 2.942676 31.9812592 77.102353 150.357224 401.529278 3943.6546 0.9997612
times_uncensored_sampled[3] 113.426420 1.849959973 112.2518639 2.877944 34.1400552 79.347520 156.244317 414.561044 3681.8192 0.9993805
times_uncensored_sampled[4] 111.518056 1.753087951 110.7728501 2.541087 31.9003489 77.392601 155.248452 404.519113 3992.6317 0.9995715
times_uncensored_sampled[5] 110.489787 1.734258261 109.5692159 2.956307 32.8630605 76.205704 152.836729 406.652097 3991.6234 0.9996255
times_uncensored_sampled[6] 111.379860 1.721726409 110.9651164 2.747596 31.9850964 77.994357 154.640477 406.163409 4153.7912 0.9995824
times_uncensored_sampled[7] 110.303823 1.760817980 110.4861524 2.892333 32.1325146 76.248466 151.848846 401.235327 3937.1936 1.0006718
times_uncensored_sampled[8] 110.140183 1.783837678 107.5528470 3.279413 33.6761498 77.219346 154.925368 397.697080 3635.2406 0.9995725
times_uncensored_sampled[9] 109.168923 1.809698699 109.9572607 2.895837 30.9878137 75.001860 150.497153 406.308839 3691.7754 1.0003221
times_uncensored_sampled[10] 110.872299 1.783161430 111.2854160 2.691868 30.8370041 78.032111 154.346484 406.452319 3894.8899 0.9992723
times_uncensored_sampled[11] 108.614731 1.714965970 109.1200621 2.739307 31.6455188 72.797807 151.442040 404.740169 4048.5378 0.9998170
times_uncensored_sampled[12] 107.751061 1.717535935 108.0197067 2.284966 31.0340227 75.589581 148.293648 402.546166 3955.4356 0.9993178
times_uncensored_sampled[13] 110.446129 1.765959811 111.8814696 3.155630 32.1957111 75.587362 152.199114 401.397368 4013.7904 0.9998564
times_uncensored_sampled[14] 109.851551 1.684822463 107.5349108 2.461176 32.4178990 76.389589 153.817899 411.342804 4073.7153 0.9993718
times_uncensored_sampled[15] 109.857209 1.778466944 110.6395773 2.679260 30.9008183 77.259022 152.222422 411.104903 3870.1645 1.0002699
times_uncensored_sampled[16] 111.521543 1.775551304 113.4907789 3.076941 31.0764767 77.529074 154.576551 413.689984 4085.5893 0.9996635
times_uncensored_sampled[17] 109.533705 1.753209617 108.8983408 2.792509 30.4546584 74.032467 153.172218 398.911966 3858.1121 0.9999021
times_uncensored_sampled[18] 110.536137 1.742304264 108.1530566 2.778019 33.1963248 78.437690 154.113070 391.458787 3853.2714 1.0003456
times_uncensored_sampled[19] 112.105289 1.862677732 114.6761120 2.665644 31.1198078 75.347735 153.828943 417.337405 3790.2729 1.0004675
times_uncensored_sampled[20] 111.033085 1.726208336 109.4573344 3.049620 33.3502072 78.520206 152.344597 395.436750 4020.7152 1.0000035
times_uncensored_sampled[21] 112.808355 1.777414708 112.5051853 2.686877 31.7530067 77.217544 157.903343 401.771585 4006.5221 1.0010791
times_uncensored_sampled[22] 107.263882 1.728249939 105.4537221 2.796784 29.9890421 75.324604 150.604945 390.356054 3723.1516 1.0016366
times_uncensored_sampled[23] 107.765321 1.664512886 107.0343802 2.651122 30.7192600 76.299133 147.507777 403.303651 4134.9692 0.9993020
times_uncensored_sampled[24] 112.200410 1.885444569 116.9103943 2.601950 30.4701118 73.913592 153.237883 431.050720 3844.8439 1.0005974
times_uncensored_sampled[25] 110.411238 1.694177390 110.3801867 2.932642 32.1849003 77.628451 151.706144 409.119324 4244.8709 0.9998554
times_uncensored_sampled[26] 108.115141 1.752860761 108.3880593 2.603952 31.9384291 74.843911 147.521999 399.156622 3823.5612 1.0005519
times_uncensored_sampled[27] 113.482701 1.802322905 114.6432290 2.689389 33.1227817 79.116924 154.441403 420.695448 4046.0535 0.9998846
times_uncensored_sampled[28] 109.524845 1.721309562 107.6252332 2.797975 33.0563720 76.803375 151.986126 399.006433 3909.4013 1.0003794
times_uncensored_sampled[29] 111.326963 1.710138092 110.8363535 2.746640 30.9949468 76.559484 155.515121 402.621589 4200.5107 0.9995621
times_uncensored_sampled[30] 111.445665 1.735606568 110.9255435 2.594088 32.0396229 76.187800 156.173695 408.121239 4084.7037 0.9996115
times_uncensored_sampled[31] 111.497230 1.804126234 113.9994517 3.006406 32.9165805 76.719974 152.223126 404.430214 3992.7460 0.9999687
times_uncensored_sampled[32] 109.973088 1.808792628 108.1405466 2.715255 31.7573398 77.876527 151.955820 386.602260 3574.3705 0.9999782
times_uncensored_sampled[33] 112.509098 1.820472335 114.8569769 3.357583 32.1200884 75.867538 155.184766 422.560379 3980.5822 0.9999326
times_uncensored_sampled[34] 111.202707 1.812667159 111.9106826 2.813270 31.8166825 76.914664 154.406809 421.565398 3811.5968 0.9995151
times_uncensored_sampled[35] 108.512073 1.737431921 109.1811660 2.733623 31.2872658 76.841191 149.377073 389.790491 3948.9339 1.0006845
times_uncensored_sampled[36] 111.919565 1.829747433 113.3388514 2.447820 31.6047749 75.570446 157.224558 394.496658 3836.8544 0.9994711
times_uncensored_sampled[37] 108.075554 1.681937695 107.9720988 2.744366 31.3584720 74.306837 152.074521 403.119623 4121.0063 0.9997310
times_uncensored_sampled[38] 111.255677 1.777698393 109.1985578 2.993910 33.6250527 77.630468 153.058268 393.383205 3773.2679 0.9998253
times_uncensored_sampled[39] 109.476718 1.754071806 109.3698931 2.895279 31.0399812 77.205963 150.824692 410.695089 3887.7725 0.9996770
times_uncensored_sampled[40] 110.227257 1.759071822 111.8466903 3.227610 30.7768954 76.092770 151.127151 407.947908 4042.7709 1.0000989
times_uncensored_sampled[41] 110.650918 1.786519298 108.0703837 2.647763 31.9845630 77.195985 153.455977 403.500915 3659.2996 1.0002175
times_uncensored_sampled[42] 111.081862 1.785876584 109.0910740 2.814263 32.6088093 77.707271 151.508503 400.600482 3731.4321 0.9997544
times_uncensored_sampled[43] 111.169415 1.753397545 112.1931368 2.925158 31.8670852 76.628954 152.206426 418.865781 4094.2258 0.9993296
times_uncensored_sampled[44] 111.357828 1.757520669 109.4285781 3.112647 33.5807523 78.519074 153.669871 408.806892 3876.6860 0.9999278
times_uncensored_sampled[45] 109.559247 1.753297335 107.7614547 3.041875 32.4959102 76.198042 153.331570 393.768321 3777.5981 1.0001621
times_uncensored_sampled[46] 110.953080 1.725286819 110.0388847 2.327364 32.8589806 78.155389 156.436811 406.841820 4067.8952 1.0004489
times_uncensored_sampled[47] 109.859547 1.727873723 107.8828646 3.400309 32.9383132 77.368959 151.646110 388.054948 3898.3510 0.9998799
times_uncensored_sampled[48] 108.627840 1.740874850 107.8691616 2.735588 30.5364309 74.905215 152.630884 387.862475 3839.3659 0.9998693
times_uncensored_sampled[49] 110.685262 1.765278387 111.0702672 2.681748 32.3622746 74.193306 153.345279 418.138419 3958.8516 1.0005514
times_uncensored_sampled[50] 112.541384 1.837123518 113.3787657 2.718055 30.9911499 77.122071 157.404537 415.370582 3808.7874 1.0006833
times_uncensored_sampled[51] 110.272434 1.772896065 110.4264132 2.842937 30.9161239 76.971293 151.734726 421.025711 3879.5324 0.9992347
times_uncensored_sampled[52] 111.848450 1.697761146 109.8010832 3.086877 33.6873636 79.807905 156.504981 396.017333 4182.7323 0.9993325
times_uncensored_sampled[53] 112.725091 1.849761112 114.2522829 2.687336 32.0840001 78.008117 152.939989 422.030882 3815.0346 1.0007891
times_uncensored_sampled[54] 110.803157 1.777886979 109.5345466 2.945389 33.0859221 77.181682 153.197194 401.643052 3795.7179 1.0002902
times_uncensored_sampled[55] 112.038439 1.833409988 116.2085336 2.640620 31.0358126 76.289710 154.537751 419.398046 4017.5090 0.9999060
times_uncensored_sampled[56] 111.366501 1.727555032 110.0425759 2.430789 32.6863896 77.323847 155.611207 397.449894 4057.4924 1.0001887
times_uncensored_sampled[57] 109.565972 1.716767016 109.6574808 2.546632 33.2929529 75.676839 147.837813 403.100448 4079.9403 0.9995424
times_uncensored_sampled[58] 109.235744 1.710481644 109.0942930 3.236615 30.4756615 76.508599 151.574146 408.095332 4067.8715 0.9999103
times_uncensored_sampled[59] 108.341945 1.707131260 108.2617664 2.262560 29.7650202 74.370331 151.489971 401.234139 4021.7622 0.9998265
times_uncensored_sampled[60] 112.765742 1.831698199 110.9808787 3.000064 32.4876321 79.262133 155.999320 420.843946 3671.0346 0.9993438
times_uncensored_sampled[61] 111.775700 1.742836262 108.2667440 2.872556 33.2700717 79.523216 155.814947 405.672731 3859.0195 0.9996573
times_uncensored_sampled[62] 111.253757 1.760229996 113.0650107 2.968211 30.9837297 76.754047 155.782439 410.464676 4125.8898 1.0004291
times_uncensored_sampled[63] 107.650569 1.670723448 106.0732676 3.135326 32.4372486 74.000563 149.283492 393.576998 4030.9068 0.9998148
times_uncensored_sampled[64] 109.011410 1.890274414 109.6143058 2.707542 32.1352562 75.568832 148.187682 408.938574 3362.6740 1.0001231
times_uncensored_sampled[65] 109.728007 1.683673304 107.6242184 2.908873 32.6687728 76.213867 152.833072 408.392643 4086.0565 1.0013276
times_uncensored_sampled[66] 112.054583 1.843987187 113.7809461 2.791058 31.2815880 77.187049 153.763831 417.078829 3807.3542 1.0000252
times_uncensored_sampled[67] 106.215249 1.658429929 108.3203943 2.534020 30.1993923 72.370475 145.787064 402.276428 4266.0526 1.0007775
times_uncensored_sampled[68] 109.472472 1.757499229 109.3465370 2.739911 31.8817876 77.000758 152.059420 395.438041 3870.9698 0.9998084
times_uncensored_sampled[69] 108.551538 1.748298567 110.4975854 2.530059 30.5667010 75.143227 149.410068 400.685475 3994.6099 0.9998959
times_uncensored_sampled[70] 111.389982 1.765086261 113.0628513 2.923384 31.3929162 78.120198 152.683547 413.300796 4103.0612 0.9996041
times_uncensored_sampled[71] 113.596079 1.808499710 115.8776224 2.959565 32.5851197 78.192680 155.213176 437.488071 4105.4642 0.9992187
times_uncensored_sampled[72] 110.993421 1.774971096 111.4490585 2.783190 30.9916139 75.595963 155.937988 418.715604 3942.4867 0.9999125
times_uncensored_sampled[73] 110.276387 1.768315355 110.4687237 2.419073 31.4446728 74.082837 151.952028 401.143114 3902.6467 1.0007533
times_uncensored_sampled[74] 110.808074 1.709115995 110.9046938 3.353438 31.1568073 77.553202 153.941526 401.650237 4210.7240 0.9992156
times_uncensored_sampled[75] 111.834532 1.758146915 112.2154885 2.606016 30.8782402 75.625542 155.351128 423.501910 4073.7585 1.0001040
times_uncensored_sampled[76] 109.591634 1.734164894 108.6899020 2.801385 32.5992710 77.252232 149.872330 414.351375 3928.2364 0.9999127
times_uncensored_sampled[77] 111.242330 1.736455438 109.1999985 3.364447 33.4448918 77.636131 153.565805 389.837950 3954.7404 0.9997231
times_uncensored_sampled[78] 111.091190 1.701696483 109.4397934 3.016364 33.2078411 75.844864 156.235710 402.941617 4136.0552 0.9995423
times_uncensored_sampled[79] 110.094686 1.701833532 110.1664836 3.080693 31.8439800 77.332826 151.779747 400.018841 4190.4901 1.0004777
times_uncensored_sampled[80] 110.094966 1.742785511 110.4757839 2.589390 31.8827203 76.263607 150.189713 395.335800 4018.3365 1.0000848
times_uncensored_sampled[81] 112.793035 1.934660761 115.7745208 2.697738 32.0473964 76.392437 153.912153 420.885489 3581.0991 1.0008772
times_uncensored_sampled[82] 109.004884 1.682663012 107.3432029 2.735050 32.6224686 76.162589 151.329958 389.878759 4069.6288 0.9999300
times_uncensored_sampled[83] 110.788675 1.745904919 108.0894958 3.456156 33.5805401 78.838787 150.651570 399.774746 3832.8851 0.9994998
times_uncensored_sampled[84] 112.286261 1.830487634 113.3139504 2.848376 30.4893818 77.773177 153.586903 421.913075 3832.0676 1.0004582
times_uncensored_sampled[85] 112.350156 1.730511694 110.3735917 2.912954 32.2518818 79.095121 158.485509 412.099086 4068.0031 0.9996667
times_uncensored_sampled[86] 111.218621 1.752484637 110.5578829 3.051175 31.6281250 77.823080 154.298339 397.592316 3979.8893 1.0015065
times_uncensored_sampled[87] 109.907808 1.762660498 110.3062060 2.733825 31.7911630 77.130368 149.606637 407.074522 3916.1791 0.9999269
times_uncensored_sampled[88] 108.437775 1.670206270 105.8529192 2.355140 33.0811240 76.241310 149.986492 397.164220 4016.6636 0.9994306
times_uncensored_sampled[89] 112.830999 1.770433411 110.1007967 2.774042 33.0003935 79.118217 156.561646 420.140474 3867.4235 0.9997485
times_uncensored_sampled[90] 110.808001 1.793460577 112.2531990 2.676612 31.2623452 76.238769 151.759007 412.320865 3917.5431 1.0010423
times_uncensored_sampled[91] 110.293719 1.740526036 109.1527616 2.791111 31.9783191 77.499408 153.548390 405.953661 3932.8593 0.9995039
times_uncensored_sampled[92] 109.892355 1.747964115 108.1488975 2.666570 32.3559505 78.567681 154.618721 400.186519 3828.0638 0.9996386
times_uncensored_sampled[93] 109.158096 1.814711713 109.9948032 2.834072 31.3697465 75.851135 151.862220 406.112898 3673.9145 1.0000557
times_uncensored_sampled[94] 110.124082 1.799533578 111.5782393 2.774552 31.2918851 75.886862 152.383453 425.478711 3844.4932 0.9999177
times_uncensored_sampled[95] 111.546125 1.744254019 109.9141666 2.807639 32.8612099 78.307635 154.903433 402.434992 3970.8902 1.0005189
times_uncensored_sampled[96] 108.924880 1.774869206 112.0284876 2.488381 31.0961337 74.183634 150.887605 404.857704 3984.0450 0.9997342
times_uncensored_sampled[97] 108.700940 1.815202320 108.7443980 2.350637 31.0534132 75.699706 149.166454 399.958052 3588.9194 1.0013870
times_uncensored_sampled[98] 111.189635 1.777586824 111.9204644 2.679688 30.2355761 76.307471 156.167158 408.759040 3964.2165 1.0002055
[ reached getOption("max.print") -- omitted 678 rows ]
exp_surv_model_draws <- tidybayes::tidy_draws(exp_surv_model_fit)
exp_surv_model_draws